Simple and versatile analytical approach for planar metamaterials

We present a simple model which permits to access the optical properties of planar metamaterials made of unit cells (meta-atoms) which are formed by a set of elementary building blocks, namely, thin metallic wires. In the model, the wires are represented as oscillating electric dipoles which are mutually coupled. The parameters describing the building blocks have to be matched once to let the model reproduce the results of a rigorous simulation or measurement. But afterwards the building blocks can be arranged in quite a different way and the achievable optical properties can be fully explored within the model without further rigorous simulations. The optical properties are accessed at normal incidence only and, for convenience, they can be described in terms of effective material tensors which are assigned to a conceptually homogenous medium causing the same optical response. As an example the model is applied to reveal the occurrence of elliptical dichroism if the split ring resonator meta-atom is modified to L- or S-shaped meta-atoms. The model constitutes an excellent tool to explore new designs of metamaterials.